### Abstract

Suppose F is a polynomial and Σ_{h≥0} F(b_{h})X^{h} represents a rational function. If the b_{h} all belong to a field finitely generated over Q, then it is a generalization of a conjecture of Pisot that there is a sequence (c_{h}) with F(c_{h}) = F(b_{h}) for h = 0, 1, . . . so that also Σ_{h≥0} c_{h}X^{h} represents a rational function. We explain the context of this Hadamard root conjecture and make some suggestions that might lead to its proof, emphasizing the apparent difficulties that have to be overcome and the ideas that might be employed to that end.

Original language | English |
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Pages (from-to) | 1183-1197 |

Number of pages | 15 |

Journal | Rocky Mountain Journal of Mathematics |

Volume | 26 |

Issue number | 3 |

Publication status | Published - Jun 1996 |

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## Cite this

Van Der Poorten, A. J. (1996). A note on Hadamard roots of rational functions.

*Rocky Mountain Journal of Mathematics*,*26*(3), 1183-1197.